The focal length f is related to the radius of curvature r of the spherical convex mirror by :

Solution

Physics sir · 3 steps

The focus sits halfway between the pole and the centre of curvature, and both lie behind a convex mirror.

1. Where the focus lies. For a spherical mirror with a small aperture, paraxial rays meet (or appear to meet) at the point midway between the pole and the centre of curvature. So in size, f = r/2.
2. Fix the sign. Use the Cartesian convention with distances measured from the pole and light travelling in the +x direction. For a convex mirror, the centre of curvature and the focus are both behind the mirror, so r and f are both positive.

   f = +r/2

3. So. The focal length is half the radius of curvature, with the same sign. For a convex mirror both are positive, so the answer is (c).

The idea to keep. For any spherical mirror, f = R/2 with f and R always having the same sign. Concave gives both negative, convex gives both positive.

Answer from the NTA final answer key. Solution by PrepWiser.